Finite Group Databasebeta

← #11928555

Subgroups — #11928555

Order 1248.

148 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×Dic6C211yesmaximal, characteristic, complemented
2C2×Dic3×D13C211yesmaximal, characteristic
3#10597664C211yesmaximal, characteristic, complemented
4C3×#6103C211yesmaximal, characteristic
5Dic3⋊Dic13C211yesmaximal, characteristic, complemented
6#10597611C211yesmaximal, characteristic, complemented
7#10597608C211yesmaximal, characteristic
8#88200—31nomaximal, Hall
9C22×C3×D13C2211yescharacteristic
10C2×C3×C4×C13C2211yescharacteristic
11C2×Dic39C2211yescharacteristic
12C2×Dic39C2211yescharacteristic
13C2×Dic3×C13C2211yescharacteristic
14C2×Dic3×C13C2211yescharacteristic
15C13×Dic6—22no—
16C2×C3×Dic13C2211yescharacteristic
17Dic3×D13—22no—
18C2×Q8×C13—31no—
19C2×C4×D13—31no—
20#6103—31no—
21#6103D311yescharacteristic
22C4⋊Dic13—31no—
23#6101—31no—
24#6101—31no—
25C22×C3×C13C2311yescharacteristic
26C2×C3×D13—21no—
27C2×C3×D13—21no—
28C2×C3×D13Q812yescomplemented
29C3×C4×C13—21no—
30Dic39—21no—
31Dic39—21no—
32C3×Dic13—21no—
33Dic3×C13—21no—
34Dic3×C13D412yes—
35C22×D13C2×D311yescharacteristic
36Q8×C13—62no—
37C2×C4×C13—31no—
38C2×C4×C13—31no—
39C2×C4×C13C2×D311yescharacteristic
40C2×Dic13—31no—
41C2×Dic13—31no—
42C2×Dic13C2×D311yescharacteristic
43C4×D13—62no—
44#878—131nomaximal, Hall
45C2×C3×C13C2×D411yescharacteristic
46C2×C3×C13C2×Q811yescharacteristic
47C2×C3×C13#4111yescharacteristic
48C3×D13—22no—
49C22×C13C22×D311yescharacteristic
50C2×D13—21no—
51C2×D13—21no—
52C2×D13Dic612yescomplemented
53C4×C13—21no—
54C4×C13—32no—
55C4×C13—61no—
56Dic13—21no—
57Dic13—61no—
58Dic13—61no—
59C22×Dic3—131no—
60C2×Dic6D1311yescharacteristic, complemented
61C3×C22⋊C4—131no—
62#217—131no—
63C4⋊Dic3—131no—
64Dic3⋊C4—131no—
65Dic3⋊C4—131no—
66C3×C13C22⋊Q811yescharacteristic, complemented, Hall
67C22⋊Q8—391noSylow
68C2×C13C2×Dic611yescharacteristic
69C2×C13D3×D411yescharacteristic
70C2×C13#23711yescharacteristic
71D13—22no—
72C23×C3—131no—
73C2×C3×C4—131no—
74C2×C3×C4C2×D1311yescharacteristic
75C2×Dic3—131no—
76C2×Dic3—131no—
77C2×Dic3—262no—
78C2×Dic3C2×D1311yescharacteristic
79C2×Dic3C2×D1311yescharacteristic
80Dic6—22no—
81C2×Q8—31no—
82C22×C4—391no—
83C4⋊C4—391no—
84C4⋊C4—391no—
85C4⋊C4—391no—
86C22⋊C4—131no—
87C22⋊C4—391no—
88C13#87811yescharacteristic, complemented, Sylow
89C22×C3—132no—
90C22×C3—261no—
91C22×C3—261no—
92C22×C3C22×D1311yescharacteristic
93C3×C4—21no—
94C3×C4—261no—
95Dic3—21no—
96Dic3—261no—
97Dic3—261no—
98Dic3C22⋊D1312yes—
99C23—131no—
100Q8—62no—
101C2×C4—31no—
102C2×C4—31no—
103C2×C4—131no—
104C2×C4—391no—
105C2×C4—391no—
106C2×C4—782no—
107C2×C4D3×D1311yescharacteristic
108C2×C3—262no—
109C2×C3Q8×D1311yescharacteristic
110C2×C3#613111yescharacteristic
111C2×C3C2×C22⋊D1311yescharacteristic
112C22—132no—
113C22—261no—
114C22—261no—
115C22C2×D3×D1311yescharacteristic
116C4—21no—
117C4—32no—
118C4—61no—
119C4—261no—
120C4—781no—
121C4—781no—
122C3#8820011yescharacteristic, complemented, Sylow
123C2—262no—
124C2Dic6×D1311yescharacteristic
125C2#1059773211yescharacteristic
126C2D3×C22⋊D1311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutator, socle, cosocleC22×C3×C13C23
FittingC2×C3×C4×C13C22
prime radicalC22×C3×D13C22
hypercenterC2×C4D3×D13
hypocenterC3×C13C22⋊Q8
LCSG ▷ C22×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×Dic6C2semidirect
3. #10597664C2semidirect
5. Dic3⋊Dic13C2semidirect
6. #10597611C2semidirect
28. C2×C3×D13Q8semidirect
52. C2×D13Dic6semidirect
60. C2×Dic6D13semidirect
66. C3×C13C22⋊Q8semidirect
88. C13#878semidirect
122. C3#88200semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C13×Dic62
C2×Dic3×D132
#105976642
C3×#61032
Dic3⋊Dic132
#105976112
#105976082
#882003
#87813